The only function of your three to have them all is 1),but 2) describes scattering states for the electrons of the atom.It doesn't annulate in asymptotic limit (r->+oO) and is not Labesgue square integrable.But it is an eigenfunction of the Hamiltonian.Because it's not normalizable,it does not fulfill the requirement expressed in the first postulate,therefore it cannot describe quantum states with discrete spectrum for the Hamiltonian.These functions can be normalized in Dirac generalized sens,implying distributions.